1. Field of the Invention
The present invention relates to a method of fabricating a reflecting mirror wherein, when a reflecting mirror utilized in, for instance, a reflecting telescope, is composed by fusing together mirror segments, the mirror segments are arranged and fused together so that the thermal deformation caused by the difference in thermal expansion coefficient among the component mirror segments, is minimized.
2. Discussion of Background
FIG. 6 is a perspective view showing a conventional reflecting mirror. In FIG. 6, a reference numeral 1 designates a reflecting mirror, which is composed by fusing together a plurality of hexagonal mirror segments (hereinafter, stacks) 2. The reflecting mirror is formed by determining the arrangement of the stacks 2 by intuition in accordance with individual cases, and by fusing them together. Furthermore, a surface of the reflecting mirror 1 is polished to form, for instance, a paraboloid or a hyperboloid with an accuracy of about 1/100 of the observed wavelength, so that visible light, or electromagnetic wave such as infrared rays emitted by a celestial body, is reflected and focused.
When the surface of the reflecting mirror 1 is provided with a complete paraboloid or the like, the incident electromagnetic wave from the celestial body geometrically converges into a point (focus). Actually, the diameter of the image of the celestial body is not nullified due to the diffraction phenomena of light. There is a theoretical limit determined by the aperture D of the reflecting mirror 1 and the wavelength .lambda. of the incident electromagnetic wave.
This theoretical limit FWHM (Full Width at Half Maximum), is generally expressed as follows. ##EQU1##
This theoretical limit is a width of an intensity distribution of light wherein the intensity becomes a half of the maximum intensity as shown in FIG. 7. Accordingly, the theoretical limit in the size of the image of a star is determined by the aperture D of the reflecting mirror 1 and the wavelength .lambda. of the incident electromagnetic wave. The larger the aperture D, the smaller the theoretical limit. Accordingly, increase in the aperture of the reflecting mirror 1 enables reduction in size of the image and hence is a significant contribution to the improvement of resolution, the improvement of limit of detection and reduction in exposure time.
However, since thermal expansion coefficients of the stacks 2 are actually not zero, the reflecting mirror 1 suffers a thermal deformation when a temperature thereof changes. When the thermal expansion coefficients of the respective stacks 2 are equal, the respective stacks 2 deform in similar figures. Accordingly, only a focus position of the reflecting mirror 1 moves, and an image formation accuracy thereof is not deteriorated. However, in practice, the stacks 2 differ from each other in thermal expansion coefficient, so that the reflecting mirror 1 is subject to irregular thermal deformation. When the aperture of the reflecting mirror 1 is large, since the number of the stacks 2 increases, the deformation becomes more complicated and the deformation quantity is enlarged even by a little inclination.
Accordingly, when such a thermal deformation is caused, the light incident from the celestial body scatter as shown in FIG. 8. The image of the celestial body is provided with an intensity distribution as shown in FIG. 9, and becomes a dim image. Therefore, even when the aperture of the reflecting mirror 1 is enlarged, the advantage of reducing the theoretical limit, can not be realized.
As major causes of the nonuniformity of the thermal expansion coefficients of the stacks 2 which causes the nonuniform thermal deformation, a difference in gradients of the thermal expansion coefficients of the respective stacks 2 in the thickness directions thereof (which causes a bimetallic deformation) and dispersing of mean thermal expansion coefficients of the respective stacks 2, are pointed out. As a method of suppressing the thermal deformation as much as possible, a stack arrangement as shown in FIG. 10, is proposed (a first conventional example).
In FIG. 10, variables .DELTA..alpha..sub.1, . . . , .DELTA..alpha..sub.37 attached to the respective stacks 2, respectively designate deviations of the mean thermal expansion coefficients of the respective stacks 2 from a mean value of the thermal expansion coefficients of all the stacks 2 (hereinafter, thermal expansion coefficient), which are classified into three groups (netting of crossing oblique lines, netting of dots, and without netting) in an order of size of the thermal expansion coefficients (.DELTA..alpha..sub.1 .gtoreq..DELTA..alpha..sub.2 .gtoreq.. . . .gtoreq..DELTA..alpha..sub.37).
In this method, around the stacks 2 belonging to a group of large thermal expansion coefficients, the stacks 2 belonging to a group of medium thermal expansion coefficients, or a group of small thermal expansion coefficients, are arranged. In this way, a large thermal expansion of the stacks 2 belonging to the group of large thermal expansion coefficients, is alleviated by a small thermal expansion of the surrounding stacks 2, by which the deformation becomes local, and it is expected by intuition that the deformation quantity becomes far smaller than in the case wherein the distribution is deviated.
FIG. 11 is a sectional diagram of a reflecting mirror provided with actuators for correcting the thermal deformation (a second conventional example), wherein a reference numeral 1 designates the reflecting mirror, 3, a temperature sensor attached to the backface of the reflecting mirror 1, 4, a processing unit for calculating a corrective force based on a measured value of a temperature of the reflecting mirror 1 obtained by the temperature sensor 3, 5, an actuator controller, and 6, the actuators for correcting the thermal deformation by applying the corrective force on the reflecting mirror 1.
In this example, when the thermal deformation is to be corrected, if one intends to totally correct it, it becomes necessary to correct even irregularities having small pitches, which requires a large correcting force and is not practical. Therefore, the deformation is expanded into a series of finite terms or infinite terms which is a function of spatial frequencies. A correction is performed by choosing terms thereof having large pitches of irregularities. At this moment, irregularities having small pitches which remain uncorrected, become a residual deformation of a mirror surface thereof which deteriorates the quality of the image.
FIG. 12 shows an arrangement of the stacks 2 wherein the thermal deformation is predicted by intuition to concentrate on the terms having large pitches of irregularities, when only the terms having large pitches of irregularities, are to be corrected. In FIG. 12, the definition of variables .DELTA..alpha..sub.1, . . . , .DELTA..alpha..sub.37 attached to the respective stacks 2, is the same as in the case of FIG. 10.
Since the conventional reflecting mirror is constructed as above, the arrangement of the respective stacks 2 is performed by intuition. Therefore, the arrangement is not necessarily the one for minimizing the thermal deformation.